Essential spectra of elementary operators

Fialkow, L. A.

doi:10.1090/S0002-9947-1981-0621980-8

Essential spectra of elementary operators
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by L. A. Fialkow

Trans. Amer. Math. Soc. 267 (1981), 157-174

DOI: https://doi.org/10.1090/S0002-9947-1981-0621980-8

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Abstract:

This paper describes the essential spectrum and index function of the operator $X \to AXB$, where $A$, $B$, and $X$ are Hilbert space operators. Analogous results are given for the restriction of this operator to a norm ideal and partial analogues are given for sums of such operators and for the case when the operators act on a Banach space.

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